Revisiting the Siegel upper half plane. I.
type: Item
instance of: scholarly article
title: Revisiting the Siegel upper half plane. I.
zbMATH Open document ID: 1047.22008
DOI: 10.1016/S0024-3795(03)00662-1
author: S. Friedland
author: Pedro J. Freitas
published in: Linear Algebra and its Applications
publication date: 2003-12-03T00:00:00Z
review text: This paper consists of two parts. The first deals with the general geometry of the Siegel upper half plane. In particular, the authors consider the compactifications of this space. Their main result is the identity of the compactification as a bounded domain and that obtained using the Busemann function. They also clarify the relationship between this boundary and the Shilov boundary. The second part of the paper is devoted to the study of discrete subgroups of the real symplectic groups, including those of infinite covolume. The authors study the limit sets of these groups and develop the theory of the critical exponents and of the Patterson-Sullivan measures for these groups, both of these with respect to \(p\)-metrics. They also consider various modifications of this concept. They obtain extensive results, for example on the non-vanishing of the critical exponents when the discrete group is ``non-elementary'', i.e. when it is not contained in any strict algebraic subgroup of the symplectic group.
Mathematics Subject Classification ID: 22E40
Mathematics Subject Classification ID: 57S30
Mathematics Subject Classification ID: 28A78
Mathematics Subject Classification ID: 58D19
zbMATH DE Number: 2012696
zbMATH Keywords: Siegel upper half plane
zbMATH Keywords: discrete groups
zbMATH Keywords: limit sets
zbMATH Keywords: Patterson-Sullivan measure
reviewed by: Samuel James Patterson
MaRDI profile type: Publication
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full work available at URL: s0024-3795(03)00662-1
OpenAlex ID: W2072047541
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description: scientific article; zbMATH DE number 2012696